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# Manipulating expressions using structure

CCSS Math: HSA.SSE.A.2

## Video transcript

- [Voiceover] So, we're sold that suppose a plus b is equal to zero. Which of these expressions equal a times b? And like always, pause the video, and see if you can figure it out. These are actually pretty fun problems. Alright, so, let's see if we can do a little bit of manipulation. So, we're told that a plus b is equal to zero. So, if we subtract b from both sides, we would get. So, if I subtract b from both sides, I would get a is equal to negative b. So, what is a time b equal to? So, a times b. Well, I could write this a few ways. I could substitute the a with a negative b, since we know a is equal to negative b. In which case, a times b would be negative b times b, which is equal to negative b squared. Another option is I could instead of saying a is equal to negative b, I could say that b is equal to negative a if we multiply both sides times negative one. So, b is equal to negative a. And so, instead of substituting a, I could substitute b with negative a. And so, this expression would be a times negative a, a times negative a, which is equal to negative a squared. So, let's see, which of these choices are there? There's a b squared, by not negative b squared. So, we see the negative a squared right over there. So, I'm feeling good. I'm feeling good about that choice.